1. What is the Angle Between Two Slopes?

The angle between two lines with slopes m1 and m2 is calculated using the tangent formula from analytical geometry. This gives the acute angle between the two lines, regardless of their orientation in the coordinate plane.

2. How Does the Calculator Work?

The calculator uses the angle between slopes formula:

Where:

• \( m_1 \) — Slope of the first line
• \( m_2 \) — Slope of the second line
• \( \theta \) — Acute angle between the lines
• The result can be in degrees or radians

Explanation: This formula derives from the tangent of the angle difference between two lines and always returns the acute angle (0° to 90° or 0 to π/2 radians).

3. Importance of Angle Calculation

Details: Calculating angles between lines is fundamental in geometry, engineering, computer graphics, and physics. It helps determine intersection angles, parallelism, perpendicularity, and relative orientations.

4. Using the Calculator

Tips: Enter the slopes of both lines (can be positive, negative, zero, or undefined as finite numbers). Select your preferred angle unit (degrees or radians). The calculator handles all valid slope combinations.

5. Frequently Asked Questions (FAQ)

Q1: What if the lines are parallel?
A: If lines are parallel (m1 = m2), the angle between them is 0° or 0 radians.

Q2: What if the lines are perpendicular?
A: If lines are perpendicular (m1 × m2 = -1), the angle between them is 90° or π/2 radians.

Q3: Can I use this for vertical lines?
A: Vertical lines have undefined slope, so this calculator requires finite slope values. For vertical lines, special cases must be handled separately.

Q4: Does the order of slopes matter?
A: No, the absolute value in the numerator ensures the angle is always positive and acute, regardless of which slope is entered first.

Q5: What's the range of possible angles?
A: The formula always returns the acute angle between 0° and 90° (0 to π/2 radians), even if the lines form an obtuse angle.